Thermodynamics

Heating with HumidificationProblems associated with the low relative humidity resulting from simpleheating can be eliminated by humidifying the heated air. This is accomplishedby passing the air first through a heating section (process 1-2) andthen through a humidifying section (process 2-3), as shown in Fig. 14–23.The location of state 3 depends on how the humidification is accomplished.If steam is introduced in the humidification section, this will resultin humidification with additional heating (T 3 T 2 ). If humidification isaccomplished by spraying water into the airstream instead, part of the latentheat of vaporization comes from the air, which results in the cooling of theheated airstream (T 3 T 2 ). Air should be heated to a higher temperature inthe heating section in this case to make up for the cooling effect during thehumidification process.AirHeatingcoilsω 2 = ω 1Chapter 14 | 7311 2 3HeatingsectionHumidifierω 3 > ω 2HumidifyingsectionFIGURE 14–23Heating with humidification.EXAMPLE 14–5Heating and Humidification of AirAn air-conditioning system is to take in outdoor air at 10°C and 30 percentrelative humidity at a steady rate of 45 m 3 /min and to condition it to 25°Cand 60 percent relative humidity. The outdoor air is first heated to 22°C inthe heating section and then humidified by the injection of hot steam in thehumidifying section. Assuming the entire process takes place at a pressureof 100 kPa, determine (a) the rate of heat supply in the heating section and(b) the mass flow rate of the steam required in the humidifying section.Solution Outdoor air is first heated and then humidified by steam injection.The rate of heat transfer and the mass flow rate of steam are to bedetermined.Assumptions 1 This is a steady-flow process and thus the mass flow rate ofdry air remains constant during the entire process. 2 Dry air and water vaporare ideal gases. 3 The kinetic and potential energy changes are negligible.Properties The constant-pressure specific heat of air at room temperature isc p 1.005 kJ/kg · K, and its gas constant is R a 0.287 kJ/kg · K (TableA–2a). The saturation pressure of water is 1.2281 kPa at 10°C, and 3.1698kPa at 25°C. The enthalpy of saturated water vapor is 2519.2 kJ/kg at 10°C,and 2541.0 kJ/kg at 22°C (Table A–4).Analysis We take the system to be the heating or the humidifying section,as appropriate. The schematic of the system and the psychrometric chart ofthe process are shown in Fig. 14–24. We note that the amount of watervapor in the air remains constant in the heating section (v 1 v 2 ) butincreases in the humidifying section (v 3 v 2 ).(a) Applying the mass and energy balances on the heating section givesDry air mass balance: m # aWater mass balance: m # 1 m # aEnergy balance: Q # ain m # 1v 1 m # 2 m # aaa h 1 m # 2v 2 S v 1 v 2a h 2 S Q # in m # a 1h 2 h 1 2The psychrometric chart offers great convenience in determining the propertiesof moist air. However, its use is limited to a specified pressure only, which is 1atm (101.325 kPa) for the one given in the appendix. At pressures other thanf1 21 = 30% 3 = 60%10°C 22°C 25°CHeatingcoilsT 1 = 10°CT 3 = 25°Cf Air· 1 = 30% f 3 = 60%V 1 = 45 m 3 /min T 2 = 22°Cf1 2 33HumidifierFIGURE 14–24Schematic and psychrometric chart forExample 14–5.